<h2>Problem 139</h2>
<div style="color:#666;font-size:80%;">27 January 2007</div><br />
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<p>Let (<i>a</i>, <i>b</i>, <i>c</i>) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such triangles together to form a square with length <i>c</i>.</p>
<p>For example, (3, 4, 5) triangles can be placed together to form a 5 by 5 square with a 1 by 1 hole in the middle and it can be seen that the 5 by 5 square can be tiled with twenty-five 1 by 1 squares.</p>
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<img src='project/images/p_139.gif' width='400' height='180' alt='' />
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<p>However, if (5, 12, 13) triangles were used then the hole would measure 7 by 7 and these could not be used to tile the 13 by 13 square.</p>
<p>Given that the perimeter of the right triangle is less than one-hundred million, how many Pythagorean triangles would allow such a tiling to take place?</p>

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